MINQUAD and MAXQUAD Statements

The NLP Procedure

MINQUAD and MAXQUAD Statements

MINQUAD H_name [ , g_name [ , c_number ] ] ;

MAXQUAD H_name [ , g_name [ , c_number ] ] ;

The MINQUAD and MAXQUAD statements specify the H, g, and c, matrices that define a quadratic objective function. The MINQUAD statement is for minimizing the objective and the MAXQUAD statement is for maximizing the objective function.

The rows and columns in H and g correspond to the order of decision variables given in the DECVAR statement. Specifying the objective function with a MINQUAD or MAXQUAD statement indirectly defines the analytic derivatives for the objective function. Therefore, statements specifying derivatives are not valid in these cases. Also, only use these statements when TECH=LINCOMP or TECH=QUADAS and no nonlinear constraints are imposed.

There are three ways of using the MINQUAD or MAXQUAD statement:

Using ARRAY Statements:
The names H_name and g_name specified in the MINQUAD or MAXQUAD statement can be used in ARRAY statements. This specification is mainly for small problems with almost dense H matrices.

  proc nlp pall;
    array h[2,2] .4 0
                  0 4;
    minquad h, -100;
    decvar x1 x2 = -1;
    bounds  2 <= x1 <= 50,
          -50 <= x2 <= 50;
    lincon 10 <= 10 * x1 - x2;
    run;

Using Elementwise Setting:
The names H_name and g_name specified in the MINQUAD or MAXQUAD statement can be followed directly by one-dimensional indices specifying the corresponding elements of matrix H and vector g. These element names can be used at the left side of numerical assignments. The one-dimensional index value l following H_name which corresponds to the element H_ij is computed by .The matrix H and vector g are initialized to zero, so that only the nonzero elements need be given. This specification is efficient for small problems with sparse H matrices.
```
  proc nlp pall;
    minquad h, -100;
    decvar x1 x2;
    bounds  2 <= x1 <= 50,
          -50 <= x2 <= 50;
    lincon 10 <= 10 * x1 - x2;
    h1 = .4; h4 = 4;
  run;
```
Using MATRIX Statements:
The names H_name and g_name specified in the MINQUAD or MAXQUAD statement can be used in MATRIX statements. There are different ways to specify the nonzero elements of matrix H and vector g by MATRIX statements. The following example illustrates one way to use the MATRIX statement .
```
  proc nlp all;
    matrix h[1,1] = .4 4;
    minquad h, -100;
    decvar x1 x2 = -1;
    bounds 2 <= x1 <= 50;
         -50 <= x2 <= 50;
    lincon 10 <= 10 * x1 - x2;
  run;
```

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